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On some generic very cuspidal representations

Part of: Lie groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  18 March 2010

Stephen DeBacker  and
Mark Reeder
Stephen DeBacker
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA (email: smdbackr@umich.edu)
Mark Reeder
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA (email: reederma@bc.edu)
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Abstract

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Let G be a reductive p-adic group. Given a compact-mod-center maximal torus S⊂G and sufficiently regular character χ of S, one can define, following Adler, Yu and others, a supercuspidal representation π(S,χ) of G. For S unramified, we determine when π(S,χ) is generic, and which generic characters it contains.

Keywords

generic representationvery cuspidalWhittaker modelMoy–Prasad depth

MSC classification

Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields 20G25: Linear algebraic groups over local fields and their integers 20G10: Cohomology theory
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 4 , July 2010 , pp. 1029 - 1055
Copyright
Copyright © Foundation Compositio Mathematica 2010

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